Abstract Enhanced index tracking is an emerging strategy for investing money in the stock market and is aimed at achieving outperformance over a given benchmark index while achieving a low tracking error. We consider the problem of rebalancing a portfolio for an enhanced index tracking strategy subject to various real-life constraints, including a lower bound and an upper bound on the expected tracking error. To solve this problem, we propose a three-phase approach consisting of preprocessing, optimization, and learning. In a computational experiment, we applied this approach to rebalance a given portfolio on a monthly basis over a time horizon of 10 years; the data for the S&P 500 benchmark index were provided by the investment company Principal Global Investors. Our approach generated portfolios that were provably close to optimality for all monthly rebalancing decisions. Over the entire horizon of 10 years, the portfolios devised by our approach yielded cumulative returns higher than the S&P 500 index after transaction costs with a moderate tracking error.

中文翻译：

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具有现实约束的增强型索引跟踪问题的三阶段方法

摘要 增强型指数跟踪是一种新兴的股票市场投资策略，旨在实现优于给定基准指数的表现，同时实现较低的跟踪误差。我们考虑为增强型指数跟踪策略重新平衡投资组合的问题，受各种现实限制，包括预期跟踪误差的下限和上限。为了解决这个问题，我们提出了一种由预处理、优化和学习组成的三阶段方法。在计算实验中，我们应用这种方法在 10 年的时间范围内每月重新平衡给定的投资组合；标普 500 基准指数的数据由投资公司 Principal Global Investors 提供。我们的方法生成的投资组合可证明对于所有月度再平衡决策都接近最优。在整个 10 年的时间里，我们的方法设计的投资组合产生的累积回报高于标准普尔 500 指数在交易成本后具有适度的跟踪误差。